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Improved Level-3 Oceanic Rainfall Retrieval from Dual-Frequency Spaceborne Radar Altimeter Systems

J. TOURNADRE Département d’Océanographie Physique et Spatiale, IFREMER, Plouzané, France

(Manuscript received 15 March 2005, in final form 28 November 2005)

ABSTRACT

Since the launch of the Ocean Topography Experiment (TOPEX)/Poseidon in 1992, several studies have demonstrated that dual-frequency altimeter measurements cannot only accurately detect rain events but can also be used to infer quantitative values. The main problems with these techniques are the limited time and space sampling of nadir-looking instruments and the uncertainty in the height of the freezing level necessary to infer the surface rain rate from the measured signal attenuation. In addition to radar altimeters, altimetric satellites carry microwave radiometers designed to correct for atmospheric water effects. Using a radiative transfer model and simplified rainy atmospheres, a method of inversion of the microwave brightness temperatures in terms of freezing level is presented. The surface rain rate is then computed from the altimeter attenuation and the radiometer freezing level. The rain climatology is computed for the three altimeters currently in operation using a mixed lognormal distribution. Comparison with the Global Pre- cipitation Climatology Project and Special Sensor Microwave Imager (SSM/I) climatologies shows that the use of freezing level greatly improves the altimeter climatology, which is of the same quality as that of the SSM/I for annual mean. The merging of the three altimeters is investigated. The resulting monthly mean rain rates are comparable to those derived from SSM/I. The high along-track resolution of altimeters also allows the determination of the length of rain events. The mean length is close to the SSM/I footprint size in the Tropics, but at higher latitude 80% of the rain has length scales smaller than 10 km, which might explain the relative underestimation of the mean rain rate by SSM/I.

1. Introduction the limited time and space sampling and the other is the uncertainty in the height of the melting layer. The melt- The determination of accurate rain-rate estimates ing-layer height, necessary to infer the surface rain rate over the global ocean has been a challenging task for from the altimeter attenuation that is integrated over over a decade. In situ rain measurements at sea are the atmospheric path, was fixed either to a constant difficult and not always reliable. Because rain is by its value (Chen et al. 1997, 2003) or to a climatological very essence a transitory phenomenon, only satellite- mean, varying with latitude and season (Quartly et al. borne instruments can provide appropriate coverage. 1999). As shown by Quartly et al. (1999), these approxi- Since the launch of the Ocean Topography Experiment mations can lead to large errors in the surface rain-rate (TOPEX)/Poseidon, the first dual-frequency altimeter estimates, especially outside of the tropical regions. to be flown in space, it has been demonstrated by vari- However, altimetric mission satellites carry, in addi- ous studies (Tournadre and Morland 1997; Quartly et tion to radar altimeters, microwave radiometers de- al. 1999; Chen et al. 1997, 2003; Cailliau and Zlotnicki signed primarily to correct the altimetric measurements 2000; McMillan et al. 2002) that this kind of instrument for the effects of atmospheric water (path delay, attenu- cannot only accurately detect rain events but also can ation, etc.). These radiometers measure brightness tem- be used to yield quantitative values. However, there are peratures (Tbs) at two or three frequencies between 18 still two main problems with these techniques—one is and 37 GHz. These frequencies are close to the ones used by the Special Sensor Microwave Imager (SSM/I) for which several algorithms have been developed to Corresponding author address: J. Tournadre, IFREMER, infer both freezing-level altitude and rain rate (Wilheit Technopole Brest-Iroise, 29280 Plouzane´, France. et al. 1977, 1991). In this study, we present a method E-mail: [email protected] that combines altimeter and radiometer data to simul-

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JTECH1897 1132 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 23 taneously estimate the melting-layer altitude and rain 1) TOPEX/POSEIDON rate. The TOPEX/Poseidon satellite was developed by the Currently, three altimeter missions are in operation, National Aeronautics and Space Administration Jason TOPEX/Poseidon, , and the Environmental Sat- (NASA) and the French Space Agency [Centre Na- ellite (Envisat). These satellites have different charac- tional d’Etudes Spatiales (CNES)]. It was launched on teristics and orbits, and thus different time and space 10 August 1992, and up to now it has provided more samplings of the global ocean. The simultaneous avail- than 12 yr of data. TOPEX/Poseidon is dedicated to ability of these three data sources gives a good oppor- ocean altimetry, and its orbit and satellite bus and pay- tunity to investigate the potential of multisatellite rain load were optimized to map the ocean surface. The climatology. The data merging requires the intercom- satellite carries two altimeters, one developed by CNES parison and the intercalibration of the freezing-level and the other by NASA. The Poseidon-1 altimeter de- and the rain-rate estimates from the different satellite veloped by CNES is a single-frequency, solid-state ex- systems. perimental instrument intended to demonstrate new A key advantage of the altimeter systems is their high technology, and it operates approximately 10% of the along-track resolution (ϳ6 km), which allows the study time. The NASA radar altimeter (NRA), which oper- of the length scales of the rain events over the global ates at 13.6 (Ku band) and 5.3 (C band) GHz simulta- ocean. The rain cell size distribution and its geographi- neously, is the primary sensor of the mission. Only the cal variability are significant and informative character- dual-frequency NRA data are considered in this study. istics for the description of rain fields (Sauvageot et al. Depending on the sea state, the altimeter footprint var- 1999). The information obtained from altimeters would ies from 5- to 10-km radius. The satellite samples the complement those obtained on land using meteorologi- ocean surface between 66°S and 66°N at a 1-s interval cal radars. The joint analysis of length scales and radi- (corresponding to a 5.8 km ground distance) for each of ometer measurements can also give insight into the ef- the 254 passes that make up a 9.9156-day repeat cycle. fect of partial beam filling and explain the differences A detailed description of the NRA instrument and data between rain estimates from the altimeter and radiom- processing is given in Zieger et al. (1991) and Marth et eter. al. (1993). In section 2, the three altimeter missions currently The satellite also carries the TOPEX/Poseidon mi- available, that is, TOPEX/Poseidon, Jason, and En- crowave radiometer (TMR), which was primarily de- visat, and the auxiliary data used for validation are signed to provide corrections for the altimeter range briefly described. In section 3, the method to infer the errors (the so-called path delay) induced by the highly freezing level and the rain rate is presented. The freez- variable atmospheric water vapor content (Ruf et al. ing-level estimates are validated by comparison to 1994; Janssen et al. 1995; Keihm et al. 1995). TMR is a those of the National Centers for Environmental Pre- modified version of the Special Sensor Microwave Ra- diction (NCEP) NWP model and SSM/I in section 4. diometer (SMMR) that flew on Seasat and Nimbus-7.It Section 5 presents the mean rain fields derived from the operates at three frequencies of 18, 21, and 37 GHz in three altimeters and also presents a comparison with a nadir-viewing direction with a footprint diameter of the ones estimated from SMM/I and the Global Pre- 43.4, 36.4, and 22.9 km, respectively (Ruf et al. 1994). cipitation Climatology Project (GPCP). The merging TMR is temporally and spatially coaligned with the of the three altimeters is also tackled in this section. TOPEX/Poseidon altimeter in order to accommodate The analysis of the distribution of the rain cell length its mission requirements. In addition to water vapor and its influence on the mean rain rate is presented in retrieval, TMR also provides useful data of cloud liquid section 6. water.

2) JASON 2. Data The CNES–NASA Jason mission is designed to en- sure the continuity of the observation and monitoring a. Dual-frequency altimeter missions: of the ocean provided by TOPEX/Poseidon and it has TOPEX/Poseidon, Jason, and Envisat basically the same characteristics. It was launched on 7 The data from the archive of the three altimeter mis- December 2001. Its main instrument is the Poseidon-2 sions, which use dual-frequency radar altimeter, have altimeter, which is derived from the experimental been used in this study. The instruments and data are Poseidon-1 altimeter. It is a compact, low-power, low- briefly presented in this section. mass instrument offering a high degree of reliability.

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The dual-frequency Poseidon-2 operates at the same level is flagged as missing. If multiple zero crossings are frequencies as the NRA, that is, at 13.6 (Ku band) and found, resulting from temperature inversions, only the

5.3 (C band) GHz. A detailed description of the Posei- lowest Z0 value is kept. don-2 altimeter is given in Ménard and Fu (2001). The Jason microwave radiometer (JMR), a Jet Pro- 2) RAIN CLIMATOLOGY pulsion Laboratory instrument of TMR heritage, is a Two types of rain climatology are used for compari- passive receiver that collects radiation emitted by the son in this study. The first is the Polar Satellite Precipi- ocean at frequencies of 18.7, 23.8, and 34 GHz, that is, tation Data Center (PSPDC) SSM/I monthly rainfall different from those of the TMR. The footprint diam- indices dataset, which is constructed using only data eters are identical to those of the TMR, that is, 43.4, from one satellite and one sensor. This dataset contains 36.4 and 22.9 km, respectively. gridded oceanic monthly total rainfall estimates as well as freezing-level altitudes. The probability distribution 3) ENVISAT functions (PDFs) method of Wilheit et al. (1991) is used The second-generation radar altimeter (RA-2) of the to derive the monthly rain indices and freezing level Envisat satellite, launched on 1 March 2002, is derived from SSM/I brightness temperatures. This dataset is a from the European Remote Sensing (ERS)-1 and ERS-2 part of the GPCP monthly rainfall products. The mean ϫ RAs, providing improved measurements and capabili- fields are provided on a 2.5° 2.5° grid covering the ties (Benveniste et al. 2001). In particular, it operates area from 65°Nto65°S, and from 0° to 360°E. not only at Ku band (13.575 GHz) like the RA, but also The second dataset is a state-of-the-art rain climatol- at S band (3.2 GHz). As for TOPEX/Poseidon, this ogy, constructed by merging different sources of in situ secondary channel is used to determine the electron and satellite data, that is, the GPCP monthly precipita- content of the atmosphere and thus to compensate the tions. The GPCP was established by the World Climate range error on altitude caused by the propagation of Research Program (WCRP) to address the problem of the radar signal through the ionosphere. Envisat is a quantifying the distribution of precipitation around the sun-synchronous satellite placed at an operating alti- globe over many years (Adler et al. 2003). The general tude of 800 km, which samples the ocean between 81°S approach is to combine the precipitation information and 81°N at a 1.1-s interval corresponding to an 8-km available from each of several sources into a final along-track distance with a repeat cycle of 35 days. De- merged product, taking advantage of the strengths of pending on the sea state, the altimeter footprint varies each data type. The microwave estimates are based on from 4- to 9-km radius. SSM/I data from the Defense Meteorological Satellite The Envisat microwave radiometer (MWR) instru- Program satellites that fly in sun-synchronous, low- ment is a derivative of the radiometers used on the earth orbits. The infrared (IR) precipitation estimates ERS-1 and ERS-2 satellites. It is a dual-channel, nadir- are obtained primarily from geostationary satellites and pointing, Dicke-type radiometer, operating at frequen- secondarily from polar-orbiting satellites. Additional cies of 23.8 and 36.5 GHz. The footprints have diam- low-Earth orbit estimates include the Television Infra- eters of approximately 20 km for both frequencies. red Observation Satellite (TIROS) Operational Verti- cal Sounder (TOVS) data and outgoing longwave radiation (OLR) precipitation index (OPI) data from the b. Auxiliary data National Oceanic and Atmospheric Administration 1) NCEP NUMERICAL MODEL (NOAA) series satellites. The gauge data are as- sembled and analyzed by the Global Precipitation Cli- The NCEP–National Center for Atmospheric Re- matology Center (GPCC) of the Deutscher Wetterdi- search (NCEP–NCAR) reanalysis data are used to cal- enst and by the Climate Prediction Center of NOAA. culate the altitude of the 0°C isotherm. The reanalysis methods and data are described in Kalnay et al. (1996). The data are archived every6honregular latitude– 3. Methods longitude grid of 2.5° grid spacing with 17 pressure lev- a. Detection of rain and rain-rate estimate els in the vertical. The freezing-level altitude Z0 is determined for every 6-h analysis by reverse interpolation The detection of rain events using dual-frequency al- of the temperature profile at each grid point to find the timeter data is well established and is currently used

Z0 geopotential height. The algorithm checks for zero operationally in the Jason and Envisat processing to crossings in the temperature profile between the 1000- flag rain-affected altimeter samples (Tournadre 2004; and 200-hPa levels. If no crossing is found, the freezing Quartly 2004). The principle has been described in de-

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FIG. 1. (a) Rain-free relation for TOPEX/Poseidon, Jason, and Envisat altimeters and (b) rms.

tail in several studies (Tournadre and Morland 1997; sure the presence of cloud liquid water, and thus to Quartly et al. 1996; Tournadre 2004). It is based on the minimize the possibility of false alarms (Tournadre and frequency dependency of rain attenuation of the elec- Morland 1997). tromagnetic signals. Basically, it detects occurrences For each detected rain event, the rain rate can be where the Ku-band (13.6 GHz) backscatter measure- estimated using the Marshall–Palmer relation (Mar- ␴ ments ( 0) are significantly attenuated compared to shall and Palmer 1948) those of the C or S band (5.3 or 3.2 GHz). In practice, ␴ ⌬␴ ͑1րb͒ the measured Ku-band 0 is compared to the Ku-band ϭ ͩ 0 ͪ ͑ ͒ ␴ R , 3 0 that should be expected from the measured C- or 2Ha ␴ S-band 0 through a rain-free relationship. For each altimeter (TOPEX/Poseidon, Jason, and Envisat) and where H is the rain height, and a and b are coefficients for each repeat cycle the rain-free Ku–C (Ku–S) rela- dependent on the frequency of the radar pulse that are ␴ derived experimentally. The same values as in Quartly tion f is determined by binning the Ku-band 0 data in intervals of 0.1 dB of C-band ␴ . The mean f(␴C/S) and et al. (1999) are used for the a and b coefficients; that is, 0 0 Ϫ1 ␴C/S a ϭ 0.0238 dB km and b ϭ 1.203. As noted earlier, standard deviation rms( 0 ) are then computed in each bin. Figure 1 presents the mean relation and rms the rain-rate estimate strongly depends on the rain for the three altimeters for 2003. The shapes of the f height, which can be assimilated to the height of the relations and of the rms are very similar for the three melting layer. For a 5-km rain height the rain detect- Ϫ1 sensors. The rms is, except for very low wind speed, less ability threshold is around 1.5 mm h . than 0.25 dB. The rain events are detected using the following cri- b. Freezing-level and rain-rate determination teria (Tournadre 2004): At microwave frequency, the ocean is a highly reflec- ⌬␴ ϭ ͑␴CրS͒ Ϫ ␴Ku Ͼ ͓ ͑␴CրS͔͒ ͑ ͒ tive background and the atmosphere is almost transpar- 0 f 0 0 min 0.5 dB, 1.8 rms 0 1 ent under most circumstances. Any atmospheric con- and stituent that absorbs and emits microwave radiation will thus increase the intensity of the upwelling radia- L Ͼ 200 ␮m, ͑2͒ z tion. Oxygen, water vapor, and liquid water absorb and ⌬␴ ␴Ku where 0 is the Ku-band rain attenuation, 0 is the emit radiation in the microwave region. In the case of ␴C/S Ku-band backscatter coefficient, and 0 is the C- or nonprecipitating clouds, the size of the water droplets is S-band backscatter coefficient. The radiometer liquid small (less than 100 ␮m) compared to the wavelength of

water content Lz is expressed as a quadratic polynomial the microwave radiation. The Rayleigh approximation of the three TMR/JMR Tbs (Keihm et al. 1995) and as applies and the absorption and diffusion are propor- a linear combination of the logarithms of the MWR Tbs tional to the cube of the droplet diameter. In case of (Benveniste 2002). This second criterion is used to en- rain, the drops are larger and the Rayleigh approxima-

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tion is no longer valid. The scattering becomes nonneg- ation, a simple method to infer the freezing level would ⌬␴ ligible and has to be included in the radiative transfer be to simply invert the 0–Tb relationships using the computations. Several radiative transfer models measured Tbs and Ku-band attenuation. However, al- (RTMs), including absorption and scattering, have timeters have much smaller footprints than radiom- been proposed and are available for rainy atmospheres eters. In case of small rain cells and/or a low rain rate, ␴ (Wilheit et al. 1977; Evans and Stephens 1995; Petty the effect of rain on an altimeter 0 can thus be much 2001; Rosenkranz 2002). In this study, the Rosenkranz larger than the effect on radiometer Tb. The use of the (2002) RTM has been chosen to model the TMR, JMR, measured attenuation to infer the freezing level from ⌬␴ and MWR Tbs for a typical rainy atmosphere. the 0–Tb relation can thus lead to an underestima- As in Wilheit et al. (1977), a Marshall–Palmer distri- tion of the freezing level. It is thus more judicious to bution of raindrops as a function of rain rate is assumed estimate the freezing level from radiometers alone by to exist from the surface up to the freezing level. A combining couples of Tb from the two lower-frequency nonprecipitating cloud of 0.25 kg mϪ2 integrated liquid channels (18 and 21 GHz for TMR, 18.7 and 23.8 GHz water content is assumed in the 0.5 km below the freez- for JMR, and 23.8 and 36.5 GHz for MWR) in a method ing level. A constant lapse rate of 6°CkmϪ1 is assumed similar to the one developed for SSM/I by Wilheit et al. in the atmosphere (U.S. Standard Atmosphere, 1976). (1991). The relative humidity is assumed to increase linearly For the altimeter samples for which rain is detected, from 80% at the surface to 100% at the freezing level. the radiometer Tbs are analyzed in terms of freezing This set of simplifying assumptions allows one to couple level. Figure 3 presents the two-dimensional histograms the freezing level, the surface temperature, and the pre- of the couple of Tbs chosen for the three radiometers. cipitable water and to reduce the number of free pa- The contours of constant rain rate and constant freez- rameters of the Tb model. The atmospheric profiles are ing level in this two-Tb space from the model are also then used as input to the Rosenkranz (2002) RTM. This given. A good proportion (35% for TMR, 35.3% for model solves the radiative transfer equation for a scat- JMR, and 28% for MWR) of the observations lies out- tering and absorbing atmosphere by numerically inte- side the model near or below the R ϭ 0mmhϪ1 con- grating an ensemble of triad functions that are con- tour. This reflects the better capability of altimeters to structed so as to satisfy the boundary conditions. A detect rain than radiometers because of their better detailed description of the model is given in Rosen- resolution and sensitivity. For example, a simple com- kranz (2002). putation shows that a small rain cell of 10-km diameter, For each frequency of the TMR, JMR, and Envisat 2mmhϪ1 rain rate, and 5-km height, centered on the radiometers, the Tbs are calculated for freezing levels satellite nadir, gives an attenuation of 0.47 dB for the varying from 0.25 to 6 km by 0.25-km steps, resulting TOPEX/Poseidon altimeter (i.e., above the detection for each freezing level in a relationship between rain threshold), but only gives a 18-GHz Tb of 163 K and a rate and Tb (R–T relationship). The R–T relationships 21-GHz Tb of 184 K, that is, below the 0 mm hϪ1 con- ⌬␴Ku are also converted into a 0 –Tb relationship using tour line. In such cases, the freezing level cannot be Eq. (3). Figure 2 presents the modeled Tbs for the 18-, directly estimated. 21-, and 37-GHz TMR channels. Similar results were In practice, for the altimeter rainy samples the Tbs found for the JMR and MWR channels. These curves are inverted in terms of freezing level and radiometer are also similar to the ones presented by Wilheit et al. rain rate by minimizing the distance between observa- (1991) for the 19- and 21-GHz SSM/I channels. We can tions and modeled Tbs. If the distance is larger than 2 see on these plots that Tb increases with attenuation K, the freezing level is flagged as invalid. As can be and freezing level. At all frequencies, the temperatures expected, the proportion of valid freezing-level esti- increase toward a maximum and then drop off as rain- mates is only about 50% for small rain rates (Ͻ3mm fall rates increase further and scattering becomes more hϪ1) but rapidly increases with rain rate to 80%–90% important. This maximum increases with freezing level for rain rates greater than 5 mm hϪ1, as can be seen in and decreases with the frequency. From the figure, it Fig. 4a. This confirms the importance of the difference can easily be seen that the lower-frequency channels of resolution between the two kinds of sensors for the are more sensitive to higher rain rates. To invert the rain detection. R–T relation in term of freezing level and rain rate, it is The freezing level for nonvalid samples is estimated thus more sensible to use the lower frequencies, which in the following way. For each month, a mean freezing are sensitive to freezing level over larger rain-rate level is computed over a 2.5° ϫ 5° grid using the valid ranges. freezing-level estimates. For each nonvalid sample, this Because the altimeter gives an estimate of the attenu- climatological freezing level is used as a proxy of the

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FIG. 2. TMR-modeled brightness temperatures as a function of altimeter Ku-band rain rate for various freezing levels (km): (a) 18-, (b) 21-, and (c) 37-GHz channels. instantaneous freezing level. The rain rate is then com- method is given in the appendix. The mean fields are puted from the freezing level and the attenuation using estimated on 2.5° latitude ϫ 5° longitude grid. relation (3).

4. Validation of freezing-level estimates c. Mean field estimate a. Comparison with NCEP freezing level The rain climatology is estimated using the same approach as that of Wilheit et al. (1991) and Berg and The radiometer’s valid freezing levels have been sys- Chase (1992) for SSM/I. A mixed probability density tematically collocated with those of NCEP for 2003. function combining a lognormal distribution describing Figure 5 presents the comparison of the two param- the positive rainfall values, and a spike at zero describ- eters. The mean latitudinal distributions show that in ing the observations indicating no rainfall are used to the Tropics (between 20°S and 20°N) the radiometer compute mean values. The detailed description of the underestimates the freezing level by about 500 m for

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FIG. 4. Proportion of valid freezing-level estimates as a function of rain rate for TOPEX/Poseidon, Jason, and Envisat.

TMR and JMR and 250 m for MWR. These results are consistent with the analysis of the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) data presented by Harris et al. (2000), which show a difference of 100–700 m between the PR bright band associated with the melting layer of precipitating clouds and the NCEP freezing level. Poleward of 30°, the radiometer freezing levels exceed those of NCEP and the differences increase with latitude, up to 1 km at 60°. Similar results are also found for SSM/I freezing-level estimates. This might result from the fact that NCEP data are averaged over 2.5° and that at midlatitudes rain is, in general, associated with the warmer air within the low pressure systems. Because we consider only the rainy samples the mean value will be biased toward higher values. The two-dimensional distributions of the collocated radiometer and NCEP freezing levels confirm the underestimation of the freezing level by radiometers for values greater than 4 km and the overestimation for value smaller than 3 km. TMR and JMR have very similar distributions except for very low levels (Ͻ1 km) for which there is a larger uncertainty. The MWR distribution is qualitatively different, especially for high FIG. 3. Bidimensional histograms (%) of brightness tempera- freezing levels where the MWR values are closer to ture from (a) TMR 18- and 21-GHz channels, (b) JMR 18.7- and 23.8-GHz channels, and (c) MWR 23.8- and 36.5-GHz channels. those of NCEP for values above 4 km. The distribution Model computation of brightness temperature as function of rain also has a larger scatter for a low freezing level (below rate and freezing level are superimposed as solid lines. 1 km). Figure 6 presents the maps of the mean freezing levels for winter 2003 for JMR, NCEP, and SSM/I satellite F13. The overall patterns of the three fields are similar,

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FIG. 5. (a) Mean latitudinal altitude of the 0°C isotherm from NCEP (Z0) (dashed line) and for TOPEX/Poseidon TMR (H0) (solid line) for the rain samples and (b) two-dimensional histogram of Z0 and H0. (c), (d) Same, but for Jason and (e), (f) Envisat. but the SSM/I field is certainly smoother than the other NCEP subtropical meridional gradient is larger in the two. Freezing-level heights in the Tropics are nearly winter hemisphere. This gradient and its north–south uniform around 4.5 km for JMR, 5 km for NCEP, and asymmetry are quite well reproduced by JMR, but not 4.75 km for SSM/I. There is a weak minimum at the so well by SSM/I. equator in the western Pacific for TMR and NCEP. The The mean latitudinal distributions of the freezing

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FIG. 6. Mean altitude of the freezing level (km) for winter 2003 from (a) Jason, (b) NCEP, and (c) SSM/I F13. level for 2003 presented in Fig. 7 show the very good NCEP. Because the principle of freezing-level determi- consistency of the three radiometer estimates because nation is essentially the same for SSM/I and the radi- their difference is always less than 250 m. The TMR and ometers, the observed differences result from the fact JMR curves are almost identical. MWR gives higher that altimeters better discriminate between rain and no- values in the Tropics. Compared to SSM/I F13, the ra- rain samples. diometer estimates are in better agreement with This analysis shows that the freezing-level estimates

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following results: ␮ ϭ 1.16 mm hϪ1 and ␴2 ϭ 0.21 for TOPEX/Poseidon, ␮ ϭ 1.12 mm hϪ1 and ␴2 ϭ 0.19 for Jason, and ␮ ϭ 1.22 mm hϪ1 and ␴2 ϭ 0.22 for Envisat. To complete this statistical analysis, the data have been systematically collocated. For Jason and TOPEX/ Poseidon, it can be easily done because during the tan- dem mission the two satellites were put on the same orbit with 1-min time separation for calibration and validation purposes. Figure 9 presents the two- dimensional histograms of the freezing-level and rain- rate estimates from the two satellites for the collocated samples (i.e., less than 5-km and 1-min separation). The mean freezing-level difference between Jason and TOPEX/Poseidon is 0.064 km with a standard deviation of 0.4 km. The correlation coefficient is 0.89. The mean rain-rate difference is 0.14 mm hϪ1 with a standard deviation of 1.4 mm hϪ1 and a correlation coefficient of 0.84. Because Envisat is placed on an orbit with very dif-

FIG. 7. Mean latitudinal altitude of the freezing level for 2003 ferent characteristics than those of TOPEX/Poseidon for TOPEX/Poseidon, Jason, Envisat, NCEP, and SSM/I F13. and Jason, and because of the very nature of rain, the number of collocated rain samples between Envisat and TOPEX/Poseidon or Jason is very limited. For 2003, from combined altimeter and radiometer data are of a only 174 Envisat–Jason collocated samples (within 30 quality at least comparable to, if not better than, SSM/I min and 25 km) were found and only 328 for Envisat– estimates when compared to NCEP data, and that they TOPEX/Poseidon. The scatterplots of rain-rate and ␴ can be used to infer rain rate for the altimeter 0 at- freezing-level estimates are presented in Fig. 10. The tenuation. mean rain-rate difference is 0.46 mm hϪ1 with a 2.45 mm hϪ1 rms for Jason rain rate and 0.20 mm hϪ1 with b. Intercomparison of altimeter rain rate and Ϫ a 2.69 mm h 1 rms for TOPEX/Poseidon. The mean freezing level freezing-level difference is 0.24 km with a 0.85-km std A statistical comparison of the rain-rate and freezing- dev for Jason and 0.18 km with a 0.78-km a standard level estimate ensembles has been conducted for the deviation for TOPEX/Poseidon. year 2003. The distributions of the two parameters for The analysis shows that TOPEX/Poseidon and Jason the three altimeters are presented in Fig. 8. The freez- give very similar rain rates and freezing levels that can ing-level distributions are almost identical for TOPEX/ be merged without any correction. The problem is Poseidon and Jason with a strong maximum at 4.5 km more complex for Envisat. The lack of a radiometer corresponding to the tropical rains. The Envisat distri- channel near 18 GHz obviously hampers the freezing- bution is very close to the two others up to 3.5 km, but level retrieval, especially in the Tropics. The occur- the peak is shifted toward 5 km and is more spread out rences of low rain rate are underestimated and those of with a much larger number of freezing levels above 4.5 average rain rate are overestimated. The collocated km. This difference of behavior results from the use of dataset is unfortunately too small to estimate a reliable the 37-GHz Tb, which saturates much faster than the calibration. The merging of Envisat data will thus re- 18-GHz Tb, resulting in an overestimation of the freez- quired the use of other techniques, such as histogram ing level for rain rates above 5 mm hϪ1. matching. The TOPEX/Poseidon and Jason rain-rate distributions are in very good agreement. However, the 5. Results TOPEX/Poseidon distribution is smoother and closer a. Mean rain rate to a lognormal distribution than that of Jason. Envisat underestimates the occurrences of rain rates smaller The three altimeter mean rain rates for 2003, esti- than3mmhϪ1, and its distribution departs more sig- mated using the method described in the appendix, are nificantly from a lognormal distribution than do the presented in Fig. 11. The corresponding GPCP and other two. The fit of a lognormal distribution gives the SSM/I climatologies are also presented in the figure.

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FIG. 8. Comparison of the TOPEX/Poseidon, Jason, and Envisat (a) rain-rate and (b) freezing-level normalized distributions.

All fields exhibit the well-known main features of the in the Atlantic and Pacific Oceans greater than in the oceanic precipitations, with maxima in the Tropics, in Southern Hemisphere circumpolar storm tracks. the intertropical convergence zone (ITCZ) in the At- It is clear from the figure that the tropical maxima lantic, Pacific, and Indian Oceans, and in the South (ITCZ, SPCZ) are underestimated by the altimeters Pacific convergence zone (SPCZ). Marked dry zones in compared to GPCP and SSM/I. This result confirms the eastern parts of the subtropical oceans are evident. that of Quartly et al. (1999) who found an underesti- The Pacific ITCZ is a narrow band slightly north of the mation of about 25% of the mean rainfall by TOPEX/ equator with peaks in both the eastern and western Poseidon in the Tropics. However, it should be noted parts of the ocean. The Atlantic Ocean ITCZ maximum that the SSM/I rain rates (used to compute the GPCP is weaker and the Indian Ocean feature extends west- ones) are corrected for partial beam filling by about ward from the north of the equator near Sumatra to the 30% in the Tropics (Adler et al. 2003). The difference south of the equator near the Seychelles Island. In the between GPCP and altimeters is maximal in the Pacific midlatitudes, the storm tracks in the Northern Hemi- warm pool and in the eastern tropical Indian Ocean sphere Ocean are clearly visible with maximum values where it can locally reach 3.5 mm dayϪ1. In the SPCZ,

FIG. 9. Comparison of the TOPEX/Poseidon and Jason two-dimensional histograms of the TOPEX/Poseidon and Jason (a) freezing levels and (b) rain rates for collocated samples.

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FIG. 10. Comparison of the Envisat and TOPEX/Poseidon (Jason) (a) rain rate and (b) freezing-level altitude for collocated samples. the underestimation is lower and does not exceed 2.5 altimeters, but some of the smaller-scale features, for mm dayϪ1. example, within the Pacific ITCZ (near 180° or 110°W), The interesting feature in the altimeter fields is the are consistent between the three altimeters, which have presence of much smaller-scale features than in the different time and space samplings. They are not arti- other two climatologies. These features might certainly facts of the sampling scheme but are real features that result in part from the undersampling of the ocean by are smoothed by SSM/I. Some of these features, for

Ϫ FIG. 11. Mean rain rate (mm day 1) for 2003 from (a) TOPEX/Poseidon, (b) Jason, (c) Envisat, (d) merged, (e) GPCP, and (f) SSM/I F13.

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Fig 11 live 4/C AUGUST 2006 T O URNADRE 1143

FIG. 12. Mean latitudinal rain rate for 2003 for (a) TOPEX/Poseidon, Jason, Envisat, and corrected Envisat and (b) GPCP and SSM/I F13 and merged altimeters. example, the relative minimum in the Pacific ITCZ Hemisphere. Considering the relatively small number near the date line, are also present in the mean annual of samples used for altimeter climatology compared to rain rate estimated from the TRMM precipitation radar those of GPCP and SSM/I, the agreement is remark- (Schumacher and Houze 2003). able. The main difference between the altimetric and The Northern Hemisphere storm tracks are narrower GPCP distribution is almost a constant bias of about in the altimeter fields and they present higher maxima 0.75–1mmdayϪ1 for latitude below 30°N. In the North- than in the SSM/I. The southern ocean storm track also ern Hemisphere, the GPCP and altimeter distributions presents higher maxima and smaller-scale structures are almost identical. than SSM/I. However, these features are not all consis- Compared to the results presented by Quartly et al. tent between the sensors. At higher latitudes, the prob- (1999, cf. our Fig. 12 to their Fig. 10), the simultaneous ability of rain is lower than in the Tropics and the un- determination of rain rate and freezing level clearly dersampling by altimeter is more important. improves the altimeter rain climatology, especially at The mean latitudinal rain rates for 2003 presented in midlatitudes where the mean altimetric rain fields of Fig. 12 show the good agreement between the three Quartly et al. (1999) were only 50% of that of GPCP. altimeters. The difference between Jason and TOPEX/ The comparison with the results of Chen et al. (2003) Poseidon is only noticeable in the Southern Ocean (top panel of their Fig. 5) is more difficult because of where TOPEX/Poseidon is about 0.5 mm dayϪ1 lower. the different approach they choose to estimate the Envisat gives larger values, in particular in the North- mean rain rate. They use a joint TOPEX/Poseidon– ern Hemisphere (by about 1 mm dayϪ1) and in the TMR precipitation index where the weights on the al- ITCZ (by about 0.5 mm dayϪ1). The altimeter distribu- timeter and radiometer indexes are latitude dependent. tions have the same structure as those of the GPCP and The final precipitation index is then adjusted to match SSM/I, that is, a narrow peak corresponding to the the GPCP distribution. Therefore, they achieve a quite ITCZ near 5°–10°N, a secondary maximum south of the good agreement between the TOPEX/Poseidon–TMR equator, and a midlatitude band for the Northern and GPCP latitudinal distribution. The main drawback

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TABLE 1. Comparison between altimeter and Global Precipitation Climatology Project mean annual rain rate for 2003.

Envisat TOPEX/Poseidon Jason Envisat corrected Merged Bias 0.16 0.69 0.56 0.50 0.55 Std dev 1.31 1.16 1.20 1.12 0.89 Min Ϫ9.1 Ϫ9.6 Ϫ5.1 Ϫ6.9 Ϫ3.6 Max 4.9 4.6 7.4 4.9 5.1 Correlation 0.804 0.820 0.805 0.829 0.889 of this method is that by using such a statistical method Jason as can be seen in Fig. 12. This is especially no- no instantaneous rain rate can be estimated. ticeable in the Northern Hemisphere where the 1 mm This analysis of the altimeter mean annual rain rate dayϪ1 gap is reduced to almost zero. shows a good agreement with existing rain climatolo- The merged rain mean field is estimated by combin- gies. It also shows that the quality of the rain-rate esti- ing all available data from TOPEX/Poseidon, Jason, mates from dual-frequency altimeters is comparable to and corrected Envisat in one dataset and fitting a log- those of SSM/I, and that they can supply useful infor- normal distribution as described in the appendix. The mation in the construction of merged climatology. The statistical comparison of the mean annual rain-rate low time and space sampling of the ocean by altimetric fields presented in Table 1 shows that merging im- mission is compensated by the high along-track resolu- proves the rms and the correlation with GPCP mean tion and by the fact that we can combined the coinci- rain rates. The bias for the merged field is about 0.55 dent and complementary active and passive microwave mm dayϪ1 with an rms of 0.88 mm dayϪ1 and a corre- data to produce the rain-rate estimates. lation of 0.889. The improvement is more sensitive for monthly rain b. Merging the altimeter datasets rate. Figure 13 presents the rms and correlation between altimeter and GPCP monthly rain rate. The rms As stated by Quartly et al. (1999), one of the main is reduced by more than 40% for the merged mean rain problems of rain climatology from altimeter is the lim- rate and the correlation, which is about 0.3–0.55 for an ited spatiotemporal sampling of the ocean by nadir- individual altimeter, and increases to more than 0.6 for looking instrument. The launches of Jason and Envisat, the merged dataset. and the continuing operation of TOPEX/Poseidon give us the opportunity to test on real data the potential of a multisatellite rain climatology. For TOPEX/Poseidon c. Analysis of rain event lengths—Influence of and Jason, their similar instrument designs and choices sensor resolution of orbit, as well as the results of their intercomparison, One of the advantages of the high along-track reso- show that they can be merged without any correction. lution of altimeters is to allow the study the distribution For Envisat, there are significant differences in the of rain cell size. The length of the rain event is deter- rain-rate and freezing-level distributions. Because of mined by the number of consecutive samples that are the limited size of the collocated Envisat and TOPEX/ detected as rainy by the altimeter. The distribution of Poseidon or Jason samples, it is not possible to inter- rain cell size is a very significant and informative char- calibrate the rain-rate estimates directly. We choose to acteristic for the description of rain fields. However, intercalibrate the Envisat rain by using the histogram- few data are available on this subject in the literature, matching technique. especially over the ocean. Studies based on altimeter Let F(R) be the cumulative normalized histogram of data cannot be as precise as the ones that can be con- the Envisat rain rates. The desired calibration trans- ducted using meteorological radar data or TRMM be- form T(R) is determined so that cause of the larger altimeter footprint but they allow

T͑R͒ investigation of the global ocean. Most of the authors F ͑R͒ ϭ ͵ G͑s͒ ds, ͑4͒ (see Sauvageot et al. 1999 for a review) have proposed 0 an exponential form for the rain cell diameter distribu- where G is the Jason cumulative normalized histogram tion (RCDD); that is, of rain rate and T is determined by a lookup table. ͑ ␶͒ ϭ ͑␶͒ ͓Ϫ␭͑␶͒ ͔ ͑ ͒ N D, N0 exp D , 5 The use of the T calibration relation significantly di- minishes the differences between the mean annual rain where D is the diameter of the equivalent circular cell rate computed from Envisat and TOPEX/Poseidon and area where the rain rate is above the threshold ␶; N(D)

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FIG. 13. (a) Correlation and (b) rms between altimeter and GPCP monthly rain-rate fields.

␶ Ϫ1 is the number of cells having diameter D, and N0( ) and 0.04 km . This corresponds to a mean chord of 25 km ␭(␶) are the two distribution parameters. For such a and a mean rain cell diameter of 16 km. In this region, distribution, the mean diameter is 1/␭. Altimeters can- deep convection enables the development of large rain not directly measure rain cell diameters, but they give cells. In the tropical Pacific, the mean chord is longer in an estimate of rain cell chords, that is, an altimeter the middle and the east of the basin than in the west performs a random sampling of rain cells; the chords (the warm pool), where the rainfall is the highest. This are the intersects of the altimeter ground tracks with feature is in good agreement with the analysis of the the rain cells. The relation between the RCDD and the horizontal structure of precipitation from TRMM data rain cell chord distribution (RCCD) has been com- presented by Nesbitt et al. (2004) who found a larger puted by Sauvageot et al. (1999). They showed that the fractional contribution of large and deep rain cells in RCCD also follows an exponential distribution whose the eastern and central tropical Pacific than in the warm slope l is related to that of the RCDD by pool. The slope increases with latitude to about 0.1 kmϪ1 in 2 the Northern Hemisphere and to about 0.15 kmϪ1 in l ϭ ␭. ͑6͒ ␲ the Southern Ocean. In the northern Pacific and Atlan- tic Oceans, there is evidence that the mean rain diam- The rain cell chords estimated by Jason and TOPEX/ eter is larger in the western part of the basins. It is Poseidon (which have the same sampling characteris- possible that this asymmetry is due to development of tics) have been analyzed for 2003 over a 5° ϫ 5° grid. storms in the western side of the ocean and their decay For each grid cell, the RCCD is estimated from the in the eastern side. In the Southern Ocean, the mean Jason and TOPEX/Poseidon datasets and is then fitted chord is close to the altimeter resolution (5.8 km), in- by an exponential distribution. Figure 14 presents the dicating the predominance of small showers. In these slope of the RCCD for 2003. In the Tropics, between regions, larger-resolution instruments such as SSM/I 20°S and 20°N, the slope shows little variability around will certainly detect fewer rain events than altimeters,

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FIG. 14. Slope of the rain cell chord distribution. which can explain why at higher latitudes the altimeters rable to SSM/I resolution, the rain detection is certainly detect comparatively more rain samples than SSM/I better and it results in SSM/I giving a larger mean rain and give higher mean rain rates. rate than the altimeters. In the midlatitudes the rain The comparison of the altimeter RCDD slopes with regime is more complex and it is more difficult to results presented in the literature is difficult because clearly identify a relationship. these studies were conducted mainly over land using Another more direct way to analyze the influence of meteorological radars. However, the typical values the sensor resolution on the rain-rate estimate is the found for midlatitudes (Sauvageot et al. 1999), which analysis of the coincident liquid water content (LZ) es- range from 0.22 to 0.35 kmϪ1 for RCDD, are in overall timates from the radiometers and the altimeters. The good agreement with our results for midlatitudes (0.16– altimeter LZ is estimated from the freezing level and 0.23 kmϪ1). the rain rate by integration of the corresponding Mar- The distribution of rain cell length can help to better shall–Palmer distribution from the sea surface to the understand the influence of the sensor resolution on the freezing level. The mean ratio of the radiometer and estimation of mean rain-rate fields. The normalized dif- altimeter LZ is then computed as a function of the rain ference between the Jason and SSM/I mean annual rain cell length and rain rate. This ratio can be seen as an (Fig. 15) shows that, compared to Jason, SSM/I gives estimate of the partial beam-filling effect for a radiom- higher values in the Tropics (by about 10%–30%) and eter. Figure 16 presents the ratio for the TOPEX/ lower values in the midlatitude storm tracks by about Poseidon data. The impact of sensor resolution can 30%–50% (north of 40°N). Some patterns of the fields clearly be seen in the figure. For rain cells whose diam- are clearly related to the rain cell length distribution. eter is smaller than 20 km, that is, much smaller than The regions where SSM/I gives a lower mean rain rate the radiometer footprint (ϳ30 km), the radiometer un- correspond to regions where rain cells have a mean derestimates the LZ for all rain rates by 10%–50% and length scale smaller than the sensor resolution. This is the underestimation increases with increasing rain rate. particularly clear in the Southern Ocean storm track For small convective cells (rain rate Ն 4mmhϪ1), the (south of 40°S) and in the North Pacific. In tropical altimeter will thus gives higher rain rates than the ra- regions, where rain cells have a mean length compa- diometer.

FIG. 15. Comparison of SSM/I and Jason mean rain rate for 2003. Deviation of Jason mean rain rate from SSM/I rain rate.

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minimizing the distance between the observed and modeled temperatures. The freezing-level estimates compare well to those of the NCEP numerical model in the Tropics where the difference is about 500 m. Out- side of the tropical band, radiometers give higher freezing levels and the difference increases with increasing latitude to about 1 km at 60°. The difference is lower than the one found for SSM/I freezing-level estimates. The comparison of the three altimeter mission estimates shows that, although the radiometers use different channels, the freezing-level estimates are in very good agreement for TOPEX/Poseidon and Jason and in good agreement for Envisat. ␴ The rain rate is then computed from the altimeter 0 attenuation and the freezing level using the Marshall– Palmer relation. The mean rain rates are estimated using a mixed lognormal distribution, in an approach similar to that of Wilheit et al. (1991). The mean annual rain rate for 2003 for the three altimeters compares well FIG. 16. Mean ratio of TOPEX/Poseidon TMR radiometer liq- with those derived from GPCP and SSM/I. The general uid water content and altimeter liquid water content as a function of rain rate and rain cell length. patterns of the mean precipitation field are well reproduced. The altimeter fields present smaller-scale features than the GPCP and SSM/I fields. Some of these For rain cells whose diameter is larger than the radi- patterns, especially in the ITCZ, are consistent between

ometer resolution, the radiometer LZ is larger than the the three satellites and are in agreement with TRMM altimeter ones for moderate rain rate (Յ5mmhϪ1). For rain climatologies. They certainly reflect geophysical stratiform rain, radiometers will give higher rain rates patterns that higher-resolution instruments better re- than altimeters. For large rain rates and cell diameters, solve. The quantitative analysis of the results shows

that is, large convective cells, Lz tends to be underesti- that altimeters underestimate the mean rain rate in the mated by the radiometers, perhaps because of the Tropics by about 25%. In the midlatitudes, the altim- strong inhomogeneities of the distribution of rain eter rain rate is in agreement with GPCP. Compared to within intense convective cells. However, the results previous studies, the joint determination of freezing have to be interpreted with caution because there are level and rain rate clearly improves the mean precipi- only few such cases. tation field from altimeters, especially at mid- and high latitudes. The intercomparison of the rain-rate estimates from 6. Conclusions the three altimeters shows that TOPEX/Poseidon and In this paper, we propose a new method to estimate Jason, which have quite similar characteristics, can be rain rate from dual-frequency altimeter measurements. merged without corrections. Envisat gives somewhat The method is tested for the three dual-frequency different results with a higher proportion of high rain altimeter satellite missions actually in operation: rates. A calibration relation has been computed using TOPEX/Poseidon, Jason, and Envisat. The main im- the histogram-matching technique. The merging of the provement is the determination from the microwave three altimeters clearly improves the mean annual rain radiometer measurements of the freezing-level altitude, rates by diminishing the rms error compared to GPCP which is necessary to infer the surface rain rate from the fields and increasing the correlation. The improvement altimeter attenuation integrated over the atmospheric is even larger when considering monthly means. The path. The method to estimate the freezing level relies rms with GPCP is reduced by 50% and the correlation on the modeling of the radiometer microwave bright- is increased from 0.5 to 0.7. ness temperatures for rainy atmosphere as a function of The high resolution of radar altimeters (ϳ6 km) al- freezing level and rain rate. The freezing level is thus lows for study of the distribution of the rain cell length inferred by inverting the brightness temperatures mea- over the global ocean. The rain length distribution is sured for the two lower-frequency channels and by assumed to follow an exponential distribution. In the

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Tropics, the mean length is about 20 km and decreases p 1 P͑R, ␮, ␴͒ ϭ expͫϪ ͑ lnR Ϫ ␮͒2ͬ, R Ͼ 0, to about 6 km at midlatitude. In the Tropics, a large R␴͌2␲ 2␴2 proportion of rain cells have diameters comparable or ͑ ͒ larger than the SSM/I sensor resolution; SSM/I gives A1 thus comparatively larger mean rain rates than the al- P͑0, ␮, ␴͒ ϭ 1 Ϫ p, R ϭ 0, ͑A2͒ timeters. In the Southern Ocean, the mean rain cell length is close to the altimeter resolution and almost where p is the probability of nonzero rainfall value. The 90% of the rain cells are only one sample long. SSM/I mean and variance of the mixed lognormal distribution in this region gives comparatively a lower mean rain are expressed by rate than the altimeter. 2 E͑R͒ ϭ pˆ exp͑␮ˆ ϩ ␴ˆ ր2͒, ͑A3͒ The results of this analysis show that dual-frequency altimeters are a useful source of information for the var͑R͒ ϭ pˆ exp͑2␮ˆ ϩ ␴ˆ 2͓͒exp͑␴ˆ 2͒ Ϫ pˆ͔. ͑A4͒ study of oceanic precipitation. They can provide rain- ␮ rate estimates with a quality comparable to that of The maximum likelihood estimate of the parameters ␴ SSM/I. They are certainly not as precise as TRMM Pre- and are given by cipitation Radar measurements, but they have the ad- 1 n vantage of covering the global ocean. They are thus ␮ˆ ϭ ͚ lnR , ͑A5͒ n i very complementary to the existing systems and could iϭ1 be used either in the merging process to produce GPCP n 1 climatology or as independent validation datasets. ␴ˆ 2 ϭ ͚ ͑lnR Ϫ ␮ˆ ͒2, ͑A6͒ n i The archive of dual-frequency altimeter data is now iϭ1 more than 13 yr long. The complete archive of the three where the Ri are the ensemble of instantaneous rainfall satellites has been processed and the results will be estimates for a given cell of the grid. distributed by the CERSAT data center in the near future (see information online at http://www.ifremer.fr/ REFERENCES cersat). Adler, R., and Coauthors, 2003: The version-2 Global Precipita- Acknowledgments. The NCEP reanalysis data used tion Climatology Project (GPCP) monthly precipitation in this study were provided by the NOAA–CIRES Cli- analysis (1979-present). J. Hydrometeor., 4, 1147–1167. Benveniste, J., Ed., 2002: ENVISAT RA2/MWR products hand- mate Diagnostics Center, Boulder, Colorado, from book. European Space Agency, ESRIN, No. PO-TN- their Web site at http://www.cdc.noaa.gov/. The SSM/I ESR6RA-0050, 382 pp. monthly rain fields were provided by the Polar Satellite ——, M. Roca, G. Levrini, P. Vincent, S. Baker, O. Zanife, C. Precipitation Data Center (PSPDC) from their Web Zelli, and O. Bombac, 2001: The Radar altimetry mission: site at http://gpcp-pspdc.gsfc.nasa.gov/. The authors RA-2, MWR, DORIS and LRR. ESA Bull., 106, 25 101– 25 108. wish to thank Dr. P. Rosenkranz who kindly provided a Berg, W., and R. Chase, 1992: Determination of mean rainfall copy of the code of his Radiative Transfer Model. The from the Special Sensor Microwave/Imager (SSM/I) using a author also wishes to thank the anonymous reviewers mixed lognormal distribution. J. Atmos. Oceanic Technol., 9, whose comments greatly helped to improve the manu- 129–141. script. Cailliau, D., and V. Zlotnicki, 2000: Precipitation detection by the TOPEX/Poseidon dual-frequency radar altimeter, TOPEX microwave radiometer, Special Sensor Microwave/Imager APPENDIX and climatological ship reports. IEEE Trans. Geosci. Remote Sens., 38, 205–213. Estimating Mean Rain Rate Chen, G., B. Chapron, J. Tournadre, K. Katsaros, and D. Vande- mark, 1997: Global oceanic precipitations: A joint view by Topex and the Topex Microwave Radiometer. J. Geophys. The method proposed Berg and Chase (1992) is used Res., 102, 10 457–10 471. to compute the spatially and temporally integrated ——, J. Ma, C. Fang, and Y. Han, 2003: Global oceanic precipi- rainfall from the instantaneous rainfall estimates from tations derived from TOPEX and TMR: Climatology and the different sensors. Rainfall is assumed to follow a variability. J. Climate, 16, 3888–3904. mixed lognormal distribution. Because there is a large Evans, K., and G. Stephens, 1995: Microwave radiative transfer probability of no-rain conditions, a lognormal probabil- through clouds composed of realistically shaped ice crystals. Part II: Remote sensing of ice clouds. J. Atmos. Sci., 52, 2058– ity for nonzero rainfall is combined with a spike at zero. 2072. The lognormal density is a nonlinear function of two Harris, G., K. Bowman, and D. Shin, 2000: Comparison of freez- variables, ␮ and ␴, ing-level altitudes from the NCEP reanalysis with TRMM

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